The height of a tree is 10-3 m- if a boy looks at the top of the tree with an angle of elevation of 30- find the distance between the boy and the tree-

The given figure illustrates the scenario mentioned in the question : Given, nbsp;the tree is having a height of 10 √(3) m. So, AB nbsp; = nbsp;10 √(3) m ...

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Mathematics

Trigonometric Ratios

The height of...

Question

The height of a tree is 10 $\sqrt{3}$ m, if a boy looks at the top of the tree with an angle of elevation of $30^{\circ}$ , find the distance between the boy and the tree.

10 m

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10 $\sqrt{3}$ m

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30 m

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20 m

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Solution

The correct option is C
30 m

The given figure illustrates the scenario mentioned in the question :
Given, the tree is having a height of $10 \sqrt{3} m .$

So, AB = $10 \sqrt{3} m .$

In Triangle ABC,
$tan 30^{\circ} = \frac{A B}{B C} = \frac{1}{\sqrt{3}} \Rightarrow B C = 10 \sqrt{3} \times \sqrt{3} \Rightarrow B C = 30 m .$

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The height of a tree is 10√3 m, if a boy looks at the top of the tree with an angle of elevation of 30∘, find the distance between the boy and the tree.

The correct option is C 30 m The given figure illustrates the scenario mentioned in the question : Given, the tree is having a height of 10√3 m. So, AB = 10√3 m. In Triangle ABC, tan30∘=ABBC=1√3⇒BC=10√3×√3⇒BC=30 m.

The height of a tree is 10 $\sqrt{3}$ m, if a boy looks at the top of the tree with an angle of elevation of $30^{\circ}$ , find the distance between the boy and the tree.